Algebraically special perturbations of the Schwarzschild solution in higher dimensions

Abstract

We study algebraically special perturbations of a generalized Schwarzschild solution in any number of dimensions. There are two motivations. First, to learn whether there exist interesting higher-dimensional algebraically special solutions beyond the known ones. Second, algebraically special perturbations present an obstruction to the unique reconstruction of general metric perturbations from gauge-invariant variables analogous to the Teukolsky scalars and it is desirable to know the extent of this non-uniqueness. In four dimensions, our results generalize those of Couch and Newman, who found infinite families of time-dependent algebraically special perturbations. In higher dimensions, we find that the only regular algebraically special perturbations are those corresponding to deformations within the Myers-Perry family. Our results are relevant for several inequivalent definitions of "algebraically special".

23 pages, no figures. v2: references added; discussion improved; matches published version

References in corpus (6)

• Robinson-Trautman spacetimes in higher dimensions
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Kerr-NUT-de Sitter Curvature in All Dimensions
• Perturbations of higher-dimensional spacetimes
• Spinor classification of the Weyl tensor in five dimensions
• Accelerating a Black Hole in Higher Dimensions

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• Duality and four-dimensional black holes: gravitational waves, algebraically special solutions, pole skipping, and the spectral duality relation in holographic thermal CFTs
• Covariant classification of conformal Killing vectors of locally conformally flat $n$-manifolds with an application to Kerr-de Sitter
• New results on the physical interpretation of black-brane gravitational perturbations
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